Jack Sock kept alive his hopes of reaching the ATP Finals knock-out stages by beating Wimbledon runner-up Marin Cilic in a final-set tie-break.
In a see-saw deciding set, the Croatian fifth seed started quickly and raced to a 3-0 lead before Sock, the eighth seed, steadied himself, cancelling out the break.
"That was a tough one for sure", Sock told Sky Sports' Annabel Croft during his on-court interview. 'It's been an interesting morning, a fire alarm went off at 4am and we all had to exit our hotel so it was a long morning. It is what it is, you have to deal with it. Marin's an incredible player, he's had an wonderful season but I was able to get through.
"My coach growing up nicknamed me 'showtime" when I was young because I loved playing in front of people. "I'm excited to excited to keep winning and keep my hopes alive this week".
The top two players from each group qualify for the semi-finals.
Later, the crowd will be treated to the latest episode in the cross-generational rivalry between Federer and Zverev, with the tournament desperately needing a compelling story after the withdrawal of world number one Rafael Nadal.
Federer, 36, and Zverev, 20, have faced each other four times and each has won twice.
The ATP Finals feature the top eight fit male singles players and doubles teams who have accrued the most points throughout the 2017 season.